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A comparison is made between a 200-ps molecular dynamics simulation in vacuum and a normal mode analysis on the protein bovine pancreatic trypsin inhibitor (BPTI) in order to elucidate the dual aspects of harmonicity and anharmonicity in the dynamics of proteins. The molecular dynamics trajectory is analyzed using principal component analysis, an effective harmonic analysis suited for comparison with the results from the normal mode analysis. The results suggest that the first principal component shows qualitatively different behavior from higher principal components and is associated with apparent barrier crossing events on an anharmonic conformational energy surface. The higher principal components appear to have probability distributions that are well approximated by Gaussians, indicating harmonicity. Eliminating the contribution from the first principal component reveals a great deal of correspondence between the 2 methods. This correspondence, however, involves a factor of 2, as the variances of the distribution of the higher principal components are, on average, roughly twice those found from the normal mode analysis. A model is proposed to reconcile these results with those from previous analyses.

We have completed an exhaustive search for the common spatial arrangements of backbone fragments (SARFs) in nonhomologous proteins. This type of local structural similarity, incorporating short fragments of backbone atoms, arranged not necessarily in the same order along the polypeptide chain, appears to be important for protein function and stability. To estimate the statistical significance of the similarities, we have introduced a similarity score. We present several locally similar structures, with a large similarity score, which have not yet been reported. On the basis of the results of pairwise comparison, we have performed hierarchical cluster analysis of protein structures. Our analysis is not limited by comparison of single chains but also includes complex molecules consisting of several subunits. The SARFs with backbone fragments from different polypeptide chains provide a stable interaction between subunits in protein molecules. In many cases the active site of enzyme is located at the same position relative to the common SARFs, implying a function of the certain SARFs as a universal interface of the protein-substrate interaction.

Fluctuations in backbone dihedral angles in the α-helical conformation of homopolypeptides are studied based on an assumption that the conformational energy function of a polypeptide consisting of n amino-acid residues can be approximated by a 2n-dimensional parabola around the minimum point in the range of fluctuations. A formula is derived that relates 〈ΔθiΔθj〉, the mean value of the product of deviations of dihedral angles ϕi and ψi (collectively designated by θi) from their energy minimum values, with a matrix inverse to the second derivative matrix F,n of the conformational energy function at the minimum point. A method of calculating the inverse matrix Fn−1 explicitly is given. The method is applied to calculating 〈ΔθiΔθj〉 for the α-helices of poly(L-alanine) and polyglycine. The autocorrelations 〈(Δϕi)2〉 and 〈(Δψi)2〉 at 300°K are found to be about 66 deg2 and 49 deg2, respectively, for poly(L-alanine), and 84 deg2 and 116 deg2, respectively, for polyglycine. The length of correlations of fluctuations along the chain is found for both polypeptides to be about eight residues long.

A theoretical analysis is given of the triple-helix–random-coil transition in a mixed solution of poly(Pro-Pro-Gly)n with two different but defined degrees of polymerization n and n′. Because of the highly cooperative nature of this helix–coil transition, each polypeptide chain tends to form a triple helix with other polypeptide chains with the same degree of polymerization (size recognition). Occurrence of triple helices consisting of polypeptide chains with different degrees of polymerization (error in recognition) is studied in detail as a function of the cooperativity, and n and n′. Implication of this analysis for molecular recognition in general is discussed.

A powerful Monte Carlo method is described to simulate thermal conformational fluctuations in native proteins by using an empirical conformational energy function in which bond lengths and bond angles are kept fixed and only dihedral angles are independent variables. In this method, collective variables corresponding to eigenvectors of the second-derivative matrix of the energy function at its minimum point are scaled according to corresponding eigenvalues in such a way that the energy function in terms of the scaled collective variables is isotropic at the minimum point. Simulation is carried out with an isotropic step size in the space of these scaled collective variables. This simulation method is applied to a small protein, bovine pancreatic trypsin inhibitor (BPTI), and its model harmonic system defined by a quadratic energy function with the same second-derivative matrix as that of BPTI at its minimum point. Efficiency of the simulation method with an isotropic step size in the space of the scaled collective variables is found to be about 500–50 times greater than the conventional method with with an isotropic step in the space of the usual nonscaled variables. One step of this new method generates conformational changes that occur in the real-time range of 0.05 ps. In a record of 5 × 105 step simulation, the BPTI molecule is observed to migrate beyond a single minimum-energy region.

By using the static correlations of fluctuations in the dihedral angles of the α-helices of polyglycine and poly(L-alanine) calculated previously, geometrical fluctuations of a section (consisting of up to 18 peptide units) of the α-helices of infinite length are calculated. These fluctuations are found to differ in some respects (e.g., the dependence of amplitudes on the length of section) from those of a circular rod made of homogeneous continuous material. However, the moduli of the mechanical strengths (tensile Young's modulus, bending Young's modulus, and the shear modulus) of a circular rod are calculated, whose geometrical fluctuations are approximately equal to the fluctuations of a section consisting of 18 peptide units. They are of the order of 1011 dyn/cm2. The tensile rigidity, flexural rigidity, and torsional rigidity are calculated to be 1.20 × 10−3 dyn, 2.46 × 10−19 dyn·cm2 and 1.79 × 10−19 dyn·cm2 for polyglycine, and 1.96 × 10−3 dyn, 4.05 × 10−19 dyn·cm2 and 3.28 × 10−19 dyn·cm2 for poly(L-alanine), respectively.

The C4N model concludes that the pocket on the complex of the anticodon bases and the discriminator base on a tRNA can accept the corresponding protein amino acid. A theoretical molecular computation by using the energy minimum principle is carried out to find the energy-refined C4N conformation. The results for Gln and Val suggest that not only the lock and key relationship but the induced fitting effect occurs. Some experiments to detect the interaction between the polynucleotides and the amino acid are being attempted.

The peripheral neuropathy associated with diabetes has characteristical histopathological findings of axonal degeneration, secondary myelin break down and atrophy. In the present study we examine structural integrity of myelin sheath in the peripheral nerves of short-term streptozotocin treated diabetic rats, using ESSR spectroscopy as a tool in determinig the dynamic state and the structure of mylein lipid phase. Experiments were performed on spin labeled sciatic and sural nerves from STZ-treated Hannover-Whitstar rats and age-matched controls. The spectrum analisys employed a numerical simulation model with the set of fitting parameters that in the same time relate the ESR line shape and the structure and dynamics of the pšrobed environment. The simulation considered threee spectral components weighted and summed in the composite spectrum. The comparative analisys of the results ahowed the fraction of the spectral component II to be significantlly increased in the spectra of diabetic rats, indicating the significant increase in overall fluidity of the myelin structure. The origin of fluidity changes was further investigated using: experimental model for demyelinzation (local injection of ethidium bromide in vivo), proteolitic action of tripsin in vitro, and osmotic myelin swelling in vitro. Analisys and comparison of the results suggested a conlusion in terms of pathologically changed biophysical properties of myelin lipid phase, that may represent the first step in development of diabetic neuropathy.